Questions and Answers
Which of the following rational numbers is the largest when placed on a number line?
If you add the rational numbers $-2/3$ and $4/9$, what is the result?
Which pair of rational numbers would result in a negative product?
Which of the following rational numbers would be positioned between $-1/2$ and $1/3$ on a number line?
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What is the result of subtracting $-5/4$ from $3/2$?
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What type of polygon has equal sides and angles, and contains 6 sides?
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When given the angle measures of a triangle as 40°, 80°, and 60°, what type of triangle can it be classified as?
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If an exterior angle of a polygon measures 120°, what is the measure of the adjacent interior angle?
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Which of the following options describes a convex polygon?
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If a product is sold for $200 after a 15% discount, what was the original price?
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Which of the following describes the relationship between rational numbers in decimal form?
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Study Notes
Comparing Rational Numbers
- To determine the largest rational number on a number line, compare the fractions using a common denominator or convert them to decimal form.
Adding Rational Numbers
- Adding −2/3-2/3−2/3 and 4/94/94/9 involves finding a common denominator.
- The common denominator for 333 and 999 is 999:
- Convert −2/3-2/3−2/3 to −6/9-6/9−6/9.
- Add −6/9+4/9=−2/9-6/9 + 4/9 = -2/9−6/9+4/9=−2/9.
Negative Product of Rational Numbers
- A negative product results from multiplying a positive rational number by a negative rational number.
- Example pairs:
- 3×−23 \times -23×−2 or −5/6×1/4-5/6 \times 1/4−5/6×1/4.
Positioning Rational Numbers on a Number Line
- Rational numbers positioned between −1/2-1/2−1/2 and 1/31/31/3 are any numbers greater than −1/2-1/2−1/2 and less than 1/31/31/3.
- Example candidates:
- 000 or −1/4-1/4−1/4.
Subtracting Rational Numbers
- Subtracting −5/4-5/4−5/4 from 3/23/23/2 can be approached as adding the opposite:
- Convert 3/23/23/2 to 6/46/46/4.
- Calculate 6/4−(−5/4)=6/4+5/4=11/46/4 - (-5/4) = 6/4 + 5/4 = 11/46/4−(−5/4)=6/4+5/4=11/4.
Measurement and Geometry (MG)
- Regular polygons have equal sides and angles, while irregular polygons do not share these properties.
- Triangle, quadrilateral, and regular polygon constructions require precise measurements using a ruler (for sides) and a protractor (for angles).
- Each polygon type has specific angle measures and side counts that define their properties.
Determining Angles and Sides
- Polygons can be analyzed by calculating angles and determining the total number of sides based on given conditions.
- Relationships exist between angle pairs, such as complementary, supplementary, and vertical angles, which help in angle measurement and classification.
Classifying Polygons
- Polygons can be classified based on the number of sides:
- Triangles (3 sides)
- Quadrilaterals (4 sides)
- Pentagons (5 sides)
- Hexagons (6 sides)
- Octagons (8 sides)
- Decagons (10 sides)
- Additional classification includes regular vs. irregular and convex vs. non-convex properties.
Exterior and Interior Angles
- The exterior angle of a polygon is equal to the sum of the two adjacent interior angles.
- The formula for the measure of each exterior angle in a regular polygon is ( 360^\circ ) divided by the number of sides.
Number and Algebra (NA)
- Percentages indicate a part of a whole and can be increased or decreased to solve various percentage problems.
- Important financial contexts for percentages include:
- Discount: Reductions in price, often expressed as a percentage of the original price.
- Commission: Earnings based on a percentage of sales or transactions.
- Sales tax: A percentage added to the price of goods/services.
- Simple interest: Calculation based on a percentage of the principal amount over time.
Rates
- Rate refers to a comparison of two quantities, often used in financial contexts, such as interest rates or exchange rates.
- A financial plan typically outlines expected income, expenses, and savings strategies, considering various rates.
- Speed can be expressed as a rate, calculated as distance over time.
Rational Numbers
- Rational numbers can be represented as fractions, decimals, or percentages, and they can be ordered on a number line according to their values.
- Operations such as addition, subtraction, multiplication, and division can be performed on rational numbers, adhering to specific mathematical rules.
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Description
This quiz focuses on ordering and performing operations with rational numbers on a number line. You will solve problems involving addition, subtraction, and comparison of various rational numbers. Test your understanding of how to manipulate these numbers accurately.
